Semiconductor device manufacturing comprises many steps of patterning layers. A layer is either the substrate of the semiconductor wafer or a film deposited on the wafer. At some steps, a pattern is etched into a layer. At some other steps, ions are implanted in a pattern into the layer. Patterning comprises: lithography, and etch or implant. The prevalent form of lithography is optical projection lithography, which involves making a mask or reticle that embodies the pattern to be projected onto the wafer; optically projecting an image of the mask onto a photoresist film coated on the wafer; exposing the photoresist; and developing the latent image, thereby making a stencil on the wafer. Other forms of lithography include: mask-less optical projection lithography where the mask is replaced by a spatial light modulator, which is driven by data representing the pattern; direct electron-beam writing lithography; and imprint lithography. All patterning processes, however faithful, distort the image to some extent. This adversely affects the performance of high-speed semiconductor devices. For example, line width variations at the gate level affect gate length, hence, speed and leakage current of CMOS transistors. Line width variations in the metal interconnection layers affect self and cross-capacitance and inductance of the interconnections. Unintentional variations in the line width limit the clock speed at which the device will function. Therefore, linewidth uniformity maps to higher revenue.
Linewidth can vary from wafer to wafer, across the wafer, across the lithography imaging field, and across the chip (die). Variations have systematic (reproducible) and random components. Minimizing the wafer-to-wafer and across the wafer variations is the object of automatic process control and automatic equipment control (APC/AEC), whereas reducing across-chip and across-field variations is best achieved by compensating the mask layout for across-field variations in the patterning process. The following processes contribute to pattern distortions. Some of these effects depend on the field position:
Mask writer position error: optical and electron-beam mask writers scan an image either in raster or vector mode. In either embodiment, electronic noise and nonlinearity in the driver circuit of the scanning system lead to random and systematic beam position errors, respectively. Mask writers move the wafer in the x and y positions, writing one swath at a time. Errors in wafer position cause stitching errors between swaths or fields.
Spreading of the mask writer beam: optical mask writers are subject to diffraction. Electron beams diverge due to the Coulomb force. Both effects spread the beam. This distortion does not depend on the position in the field, but ignoring it in mask design can cause across-chip variability.
E-beam proximity effect: In an e-beam mask writer, electrons scatter in the resist and in the mask. Scattered electrons laterally smear the exposure. The length scale of this effect is on the order of 10 μm on the mask. A software proximity correction modulates the exposure dose to compensate for the proximity effect. However, the correction is not perfect.
Fogging and flare in the mask writer: In an e-beam mask writer, secondary and backscattered electrons from the wafer scatter off parts of the e-beam column and chamber and expose the wafer. The length scale of fogging is on the order of 10 mm. Laser mask writers are subject to flare, which can be caused by multiple reflections between the interfaces of lenses and scattering from microscopic roughness of the surfaces of optical components.
Mask Etch: Etching of the chrome film on the mask depends on the average pattern density in a long-range (on the order of 1 mm). Variations in mean pattern density cause variations in the widths of features etched into chrome. Non-uniformity of silica etch-depth in phase shift masks cause phase errors.
Illumination of the lithography projector: The pupil illumination of the lithography projector has a prescribed shape such as a circle, annulus, or dipole. Either the intensity within the prescribed shape is assumed uniform, or the actual distribution is measured. If the illumination distribution differs from the one assumed during the chip design, the printed pattern will be distorted. If the pupil illumination pattern or total intensity varies across the slit of the lithography projector, this variation causes a pattern distortion that depends on the field position.
Multiple scattering at the mask: Scattering or diffraction of electromagnetic waves from a strong scatterer, such as the mask, is highly nonlinear due to multiple scattering. This effect is not position dependent but ignoring it in mask design can cause across-chip variability.
Imaging with finite aperture optics: Features of the aerial image are subject to the wave and electromagnetic field nature of light. The imaging system is a low-pass filter in the spatial frequency domain. This limits how fast light intensity can change as a function of position on the wafer. This is by far the most significant contributor to image distortion in the sub-wavelength domain. This distortion is not position dependent, but ignoring it in mask design causes strong across-chip variability.
Projection lens aberrations: Projections lenses have wavefront errors that are on the order of 1/100 of a wave. The wavefront error depends on the position in the pupil plane and on the position in the image field, a total of 4 scalar variables. Lens aberrations distort the image in a pattern and position dependent manner.
Flare in the projection lens: Any mechanism that sends a portion of a light ray in an unintended direction increases the background light level and reduces the contrast. Such mechanisms include: volume-scattering in lenses due to density variations in the lens material; surface scattering off grinding marks and other surface roughness on lens and mirror surfaces; multiple reflections between lens elements, wafer, mask, or the lens barrel. Flare depends on the position in the imaging field.
Lithography scanner position error: Lithography stepper-scanners use a slit-shaped subset of the image field to keep the lens aberrations low. The size of the slit is on the order of 26 mm by 8 mm on the wafer. The wafer and the mask are scanned in synchronization along the short dimension of the slit on the order of 33 mm at speeds up to 500 mm/s. The mask and the wafer are scanned in opposite directions and the ratio of their displacements must equal the lens magnification precisely. Relative position errors between the wafer and the image of the mask on the wafer can have random and systematic components. Random position errors blur the image.
Diffusion of reactants in the resist: After the resist is exposed, its temperature is elevated. This process is called post-exposure bake. Elevated temperature increases the diffusion coefficient of the reactants in the resist. Diffusion diminishes the contrast of the high-spatial frequency components of the image. The diffusion length, which is on the order of 30 nm, can vary across the wafer. This distortion does not depend on the position in the field, but ignoring it in mask design causes across-chip variability.
Wafer-etch: The difference in a critical dimension in the developed resist pattern and in the etched pattern is called etch-bias. Etch bias depends on the density of the pattern over a long range. This can cause an across-chip variation in the etch bias.
Optical proximity correction is a technique that compensate for some of these distortions (see A. K-T Wong, Resolution enhancement techniques in optical lithography, SPIE Press, Vol. TT47, Bellingham, Wash., 2001; H. J. Levinson, Principles of Lithography, SPIE Press, Bellingham, Wash., 2001). However, this technique does not take into account the dependence of the patterning process on the position in the imaging field.